Solve -(8a+3b-c)+(5a-6+c)+(-a-6-c)+7a-b+4c

$$- ( 8 a + 3 b - c ) + ( 5 a - 6 + c ) + ( - a - 6 - c ) + 7 a - b + 4 c$$

Evaluate

$$3a-4b+5c-12$$

Solution Steps

To find the opposite of 8a+3b-c, find the opposite of each term.

$$-8a-3b-\left(-c\right)+5a-6+c-a-6-c+7a-b+4c$$

The opposite of -c is c.

$$-8a-3b+c+5a-6+c-a-6-c+7a-b+4c$$

Combine -8a and 5a to get -3a.

$$-3a-3b+c-6+c-a-6-c+7a-b+4c$$

Combine c and c to get 2c.

$$-3a-3b+2c-6-a-6-c+7a-b+4c$$

Subtract 6 from -6 to get -12.

$$-3a-3b+2c-12-a-c+7a-b+4c$$

Combine 2c and -c to get c.

$$-3a-3b+c-12-a+7a-b+4c$$

Combine -3a and 7a to get 4a.

$$4a-3b+c-12-a-b+4c$$

Combine -3b and -b to get -4b.

$$4a-4b+c-12-a+4c$$

Combine c and 4c to get 5c.

$$4a-4b+5c-12-a$$

Combine 4a and -a to get 3a.

$$3a-4b+5c-12$$

Expand

$$3a-4b+5c-12$$

Solution Steps

To find the opposite of 8a+3b-c, find the opposite of each term.

$$-8a-3b-\left(-c\right)+5a-6+c-a-6-c+7a-b+4c$$

The opposite of -c is c.

$$-8a-3b+c+5a-6+c-a-6-c+7a-b+4c$$

Combine -8a and 5a to get -3a.

$$-3a-3b+c-6+c-a-6-c+7a-b+4c$$

Combine c and c to get 2c.

$$-3a-3b+2c-6-a-6-c+7a-b+4c$$

Subtract 6 from -6 to get -12.

$$-3a-3b+2c-12-a-c+7a-b+4c$$

Combine 2c and -c to get c.

$$-3a-3b+c-12-a+7a-b+4c$$

Combine -3a and 7a to get 4a.

$$4a-3b+c-12-a-b+4c$$

Combine -3b and -b to get -4b.

$$4a-4b+c-12-a+4c$$

Combine c and 4c to get 5c.

$$4a-4b+5c-12-a$$

Combine 4a and -a to get 3a.

$$3a-4b+5c-12$$